The planning domain has experienced increased interest in the formal synthesis of decision-making policies. This formal synthesis typically entails finding a policy which satisfies formal specifications in the form of some well-defined logic. While many such logics have been proposed with varying degrees of expressiveness and complexity in their capacity to capture desirable agent behavior, their value is limited when deriving decision-making policies which satisfy certain types of asymptotic behavior in general system models. In particular, we are interested in specifying constraints on the steady-state behavior of an agent, which captures the proportion of time an agent spends in each state as it interacts for an indefinite period of time with its environment. This is sometimes called the average or expected behavior of the agent and the associated planning problem is faced with significant challenges unless strong restrictions are imposed on the underlying model in terms of the connectivity of its graph structure. In this paper, we explore this steady-state planning problem that consists of deriving a decision-making policy for an agent such that constraints on its steady-state behavior are satisfied. A linear programming solution for the general case of multichain Markov Decision Processes (MDPs) is proposed and we prove that optimal solutions to the proposed programs yield stationary policies with rigorous guarantees of behavior.

Highly dynamic mobile ad-hoc networks (MANETs) remain as one of the most challenging environments to develop and deploy robust, efficient, and scalable routing protocols. In this paper, we present DeepCQ+ routing protocol which, in a novel manner integrates emerging multi-agent deep reinforcement learning (MADRL) techniques into existing Q-learning-based routing protocols and their variants and achieves persistently higher performance across a wide range of topology and mobility configurations. While keeping the overall protocol structure of the Q-learning-based routing protocols, DeepCQ+ replaces statically configured parameterized thresholds and hand-written rules with carefully designed MADRL agents such that no configuration of such parameters is required a priori. Extensive simulation shows that DeepCQ+ yields significantly increased end-to-end throughput with lower overhead and no apparent degradation of end-to-end delays (hop counts) compared to its Q-learning based counterparts. Qualitatively, and perhaps more significantly, DeepCQ+ maintains remarkably similar performance gains under many scenarios that it was not trained for in terms of network sizes, mobility conditions, and traffic dynamics. To the best of our knowledge, this is the first successful application of the MADRL framework for the MANET routing problem that demonstrates a high degree of scalability and robustness even under environments that are outside the trained range of scenarios. This implies that our MARL-based DeepCQ+ design solution significantly improves the performance of Q-learning based CQ+ baseline approach for comparison and increases its practicality and explainability because the real-world MANET environment will likely vary outside the trained range of MANET scenarios. Additional techniques to further increase the gains in performance and scalability are discussed.

Changepoint analysis deals with unsupervised detection and/or estimation of time-points in time-series data, when the distribution generating the data changes. In this article, we consider \emph{offline} changepoint detection in the context of large scale textual data. We build a specialised temporal topic model with provisions for changepoints in the distribution of topic proportions. As full likelihood based inference in this model is computationally intractable, we develop a computationally tractable approximate inference procedure. More specifically, we use sample splitting to estimate topic polytopes first and then apply a likelihood ratio statistic together with a modified version of the wild binary segmentation algorithm of Fryzlewicz et al. (2014). Our methodology facilitates automated detection of structural changes in large corpora without the need of manual processing by domain experts. As changepoints under our model correspond to changes in topic structure, the estimated changepoints are often highly interpretable as marking the surge or decline in popularity of a fashionable topic. We apply our procedure on two large datasets: (i) a corpus of English literature from the period 1800-1922 (Underwoodet al., 2015); (ii) abstracts from the High Energy Physics arXiv repository (Clementet al., 2019). We obtain some historically well-known changepoints and discover some new ones.

We study the problem of causal structure learning with no assumptions on the functional relationships and noise. We develop DAG-FOCI, a computationally fast algorithm for this setting that is based on the FOCI variable selection algorithm in \cite{azadkia2019simple}. DAG-FOCI requires no tuning parameter and outputs the parents and the Markov boundary of a response variable of interest. We provide high-dimensional guarantees of our procedure when the underlying graph is a polytree. Furthermore, we demonstrate the applicability of DAG-FOCI on real data from computational biology \cite{sachs2005causal} and illustrate the robustness of our methods to violations of assumptions.

The Bayesian brain hypothesis postulates that the brain accurately operates on statistical distributions according to Bayes' theorem. The random failure of presynaptic vesicles to release neurotransmitters may allow the brain to sample from posterior distributions of network parameters, interpreted as epistemic uncertainty. It has not been shown previously how random failures might allow networks to sample from observed distributions, also known as aleatoric or residual uncertainty. Sampling from both distributions enables probabilistic inference, efficient search, and creative or generative problem solving. We demonstrate that under a population-code based interpretation of neural activity, both types of distribution can be represented and sampled with synaptic failure alone. We first define a biologically constrained neural network and sampling scheme based on synaptic failure and lateral inhibition. Within this framework, we derive dropout based epistemic uncertainty, then prove an analytic mapping from synaptic efficacy to release probability that allows networks to sample from arbitrary, learned distributions represented by a receiving layer. Second, our result leads to a local learning rule by which synapses adapt their release probabilities. Our result demonstrates complete Bayesian inference, related to the variational learning method of dropout, in a biologically constrained network using only locally-learned synaptic failure rates. Introduction The Bayesian Brain hypothesis has led to a number of important insights about neural coding in the brain (Knill and Pouget, 2004; Friston, 2010, 2012; Pouget et al., 2013; Lee and Mumford, 2003) by characterizing neural representation and processing in terms of formal probabilistic inference and sampling. Furthermore, the introduction of related probabilistic representations and sampling processes in modern deep learning variational models has led to improved performance on a range of different tasks (Zhang et al., 2019; Blei et al., 2017; Kingma and Welling, 2014; Detorakis et al., 2019). The widely-used dropout technique in deep learning can be seen as a form of variational inference and sampling (Srivastava et al., 2014; Gal and Ghahramani, 2016) with direct analogy to the random failure of synapses in the brain. This link has led to biologically-motivated models of variational deep learning that use network weight dropout to simulate synaptic failure (Mostafa and Cauwenberghs, 2018; Wan et al., 2013; Neftci et al., 2016). In this paper, we build on these and other recent findings in machine learning and neurobiology to show how the brain can accurately represent the two primary components of probabilistic inference, distributions of observed data and distributions of unobserved values (such as model parameters), with the single, biologically established mechanism of synaptic failure.

Reinforcement learning (RL) agents are widely used for solving complex sequential decision making tasks, but still exhibit difficulty in generalizing to scenarios not seen during training. While prior online approaches demonstrated that using additional signals beyond the reward function can lead to better generalization capabilities in RL agents, i.e. using self-supervised learning (SSL), they struggle in the offline RL setting, i.e. learning from a static dataset. We show that performance of online algorithms for generalization in RL can be hindered in the offline setting due to poor estimation of similarity between observations. We propose a new theoretically-motivated framework called Generalized Similarity Functions (GSF), which uses contrastive learning to train an offline RL agent to aggregate observations based on the similarity of their expected future behavior, where we quantify this similarity using \emph{generalized value functions}. We show that GSF is general enough to recover existing SSL objectives while also improving zero-shot generalization performance on a complex offline RL benchmark, offline Procgen.

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In recent years, large-scale Bayesian learning draws a great deal of attention. However, in big-data era, the amount of data we face is growing much faster than our ability to deal with it. Fortunately, it is observed that large-scale datasets usually own rich internal structure and is somewhat redundant. In this paper, we attempt to simplify the Bayesian posterior via exploiting this structure. Specifically, we restrict our interest to the so-called well-clustered datasets and construct an \emph{approximate posterior} according to the clustering information. Fortunately, the clustering structure can be efficiently obtained via a particular clustering algorithm. When constructing the approximate posterior, the data points in the same cluster are all replaced by the centroid of the cluster. As a result, the posterior can be significantly simplified. Theoretically, we show that under certain conditions the approximate posterior we construct is close (measured by KL divergence) to the exact posterior. Furthermore, thorough experiments are conducted to validate the fact that the constructed posterior is a good approximation to the true posterior and much easier to sample from.

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing methodologies are limited to \textit{maximum a posteriori} estimation. The potential to perform uncertainty quantification has not yet been realized. This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement. In addition, it lends itself naturally to conduct model selection for the choice of hyperparameters. We illustrate the performance of our methodology in several computed examples, including a deconvolution problem and sparse identification of dynamical systems from time series data.

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.